[1002b]
[1]
at one
time, when they are joined one surface is instantaneously produced,
and at another, when they are divided, two. Thus when the bodies are
combined the surface does not exist but has perished; and when they
are divided, surfaces exist which did not exist before. (The
indivisible point is of course never divided into two.) And if they
are generated and destroyed, from what are they
generated?It is
very much the same with "the present moment" in time. This too cannot
be generated and destroyed; but nevertheless it seems always to be
different, not being a substance. And obviously it is the same with
points, lines and planes, for the argument is the same; they are all
similarly either limits or divisions.1In general one might wonder why
we should seek for other entities apart from sensible things and the
Intermediates:2 e.g., for the
Forms which we Platonists assume.If it is for the reason that the objects of
mathematics, while differing from the things in our world in another
respect, resemble them in being a plurality of objects similar in
form, so that their principles cannot be numerically determined (just
as the principles of all language in this world of ours are
determinate not in number but in kind—unless one takes such
and such a particular syllable
[20]
or sound, for the principles of these are
determinate in number too—and similarly with the Intermediates, for in
their case too there is an infinity of objects similar in form), then
if there is not another set of objects apart from sensible and
mathematical objects, such as the Forms are said to be, there will be
no substance which is one both in kind and in number, nor will the
principles of things be determinate in number, but in kind
only.Thus if this is
necessarily so, it is necessary for this reason to posit the Forms
also. For even if their exponents do not articulate their theory
properly, still this is what they are trying to express, and it must
be that they maintain the Forms on the ground that each of them is a
substance, and none of them exists by accident.On the other hand, if we are to assume
that the Forms exist, and that the first principles are one in number
but not in kind, we have already stated3 the impossible consequences which must follow.4(12.) Closely
connected with these questions is the problem whether the elements
exist potentially or in some other sense.If in some other sense, there will be
something else prior to the first principles.
1 For arguments against the substantiality of numbers and mathematical objects see Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.
2 Cf. Aristot. Met. 3.2.20ff..
4 This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.
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